Definition: The angle of elevation is the angle between the horizontal line of sight and the line of sight up to an object above the observer.
What is it?
You stand on level ground and look straight ahead. Then you tilt your gaze upward to the top of a tower. The angle between the two lines of sight is the angle of elevation. Looking down gives the angle of depression, measured from the horizontal downward.
Why are they linked?
The horizontal lines are parallel, so the angle of elevation from the lower point equals the angle of depression from the upper point, by alternate interior angles.
Example. From a point 85 m from the base of a cliff, the angle of elevation of the top is 33 degrees. The horizontal distance is the adjacent side, and the cliff height is the opposite side, so use tangent: height = 85 · tan 33 degrees = 85(0.6494), about 55.2 m. A person with eyes 1.6 m above the ground sees the same angle, so the cliff is about 56.8 m tall.
What errors occur?
Measuring the angle from the vertical, instead of from the horizontal. Forgetting the observer height is another frequent slip. A diagram with a right triangle almost always helps.